How to generate unknown orthogonal polynomials out of known orthogonal polynomials
type: Item
instance of: scholarly article
title: How to generate unknown orthogonal polynomials out of known orthogonal polynomials
zbMATH Open document ID: 0764.65009
DOI: 10.1016/0377-0427(92)90261-U
author: B. Fischer
author: Gene H. Golub
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-18T00:00:00Z
review text: The aim of this paper is to present algorithms for generating the three- term recursion coefficients of orthogonal polynomials for a weight function \(v(t)=r(t)w(t)\). The weight function is obtained by modifying a given weight function \(w\) by a rational function \(r\). The authors describe a modified Chebyshev algorithm and apply it to the construction of orthogonal polynomials. Three algorithms are presented for the computation of orthogonal polynomials relative to weight functions \(v\) obtained by modifying \(w\) by a linear divisor or by a quadratic divisor. Some experiments with the derived methods are presented and discussed.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 85925
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: recurrence relations
zbMATH Keywords: modified moments
zbMATH Keywords: Gauss quadrature
zbMATH Keywords: algorithms
zbMATH Keywords: modified Chebyshev algorithm
describes a project that uses: SCPACK
MaRDI profile type: Publication
cites work: Q4170993
cites work: A domain decomposition method for generating orthogonal polynomials for a Gaussian weight on a finite interval
cites work: On Generating Polynomials which are Orthogonal over Several Intervals
cites work: An Implemention of Christoffel's Theorem in the Theory of Orthogonal Polynomials
cites work: Computational Aspects of Three-Term Recurrence Relations
cites work: Minimal Solutions of Three-Term Recurrence Relations and Orthogonal Polynomials
cites work: Q3938409
cites work: Q3667838
cites work: Calculation of Gauss Quadrature Rules
cites work: On the calculation of Jacobi matrices
cites work: Numerical integration using Rys polynomials
cites work: Q3028307
cites work: Numerical Computation of the Schwarz–Christoffel Transformation
cites work: Q3257917
cites work: The connection between systems of polynomials orthogonal with respect to different distribution functions
cites work: Modified moments and Gaussian quadratures
full work available at URL: 0377-0427(92)90261-u
OpenAlex ID: W2003934994
description: scientific article; zbMATH DE number 85925